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Asymptotics of Restricted Partition Functions

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Speaker: 
Ayla Gafni
Affiliation: 
University of Mississippi
Date: 
Wed, 2021-05-05 14:30 - 15:30
Parent event: 
Number theory lunch seminar

Given a set $\mathcal A \subset \mathbb N$, the restricted partition function $p_{\mathcal{A}} (n)$ counts the number of integer partitions of $n$ with all parts in $\mathcal A$. In this talk, we will explore the features of the restricted partitions function $p_{\mathbb P_k}(n)$ where $\mathcal P_k$ is the set of $k$-th powers of primes. Powers of primes are both sparse and irregular, which makes $p_{\mathbb P_k}(n)$ quite an elusive function to understand. We will discuss some of the challenges involved in studying restricted partition functions and what is known in the case of primes, $k$-th powers, and $k$-th powers of primes.

 

Zoom Meeting ID: 919 6497 4060
For password contact Pieter Moree (moree@mpim...).

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